Digraphs of degree 3 and order close to the moore bound
نویسندگان
چکیده
It is known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist (see 20] or 5]). Furthermore, for degree 2, it is shown that for k 3 there are no digraphs of order`close' to, i.e., one less than, Moore bound 18]. In this paper, we shall consider digraphs of diameter k, degree 3 and number of vertices one less than Moore bound. We give a necessary condition for the existence of such digraphs and, using this condition, we deduce that such digraphs do not exist for innnitely many values of the diameter.
منابع مشابه
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It is known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist (see [16] or [4]). For degree 2, it has been shown that for diameter k ~ 3 there are no digraphs of order 'close' to, i.e., one less than, the Moore bound (14). For diameter 2, it is known that digraphs close to Moore bound exist for any degree because the line digraphs of complete digraphs are an example of such di...
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 20 شماره
صفحات -
تاریخ انتشار 1995